Kenneth Rosen Edition 7 Exercise 1.1 Question 2 (Page No. 12)

Question

Which of these are propositions?What are the truth values of those that are propositions?

• A. Do not pass go.
• B. What time is it?
• C. There are no black flies in Maine.
• D. 4 + x = 5.
• E. The moon is made of green cheese.
• F. $2^n \geq 100$

Answer 1

$A.$  Do not pass go.         $\Rightarrow$ Not a proposition.     Why? because it's an order.

$B.$ What is the time?      $\Rightarrow$ Not a proposition.     Why ? because it's a question.

$C.$ There are no black flies in Maine.    $\Rightarrow$ A proposition.  Why? It has truth value False.

$D.$ $4+x=5$                        $\Rightarrow$ Not a proposition.        Why?  because its truth value depends on '$x$'.

$E.$ The moon is made of green cheese.     $\Rightarrow$ a proposition.  Why? because, Its truth value is False.

$F.$ $2^n \geq 100$             $\Rightarrow$ Not a proposition. Why? because, Its truth value depends on the value of '$n$'.